Neutrinos and the Flavour Puzzlevietnam.in2p3.fr/2013/Inauguration/transparencies/Gavela.pdf[Alonso,...

Neutrinos and the Flavour Puzzle

(Alonso, Gavela, D.Hernandez, Merlo, Rigolin)

Belén Gavela

(Alonso, Gavela, Isidori, Maiani)

Cabibbo’s dream


Belén Gavela


3

Neutrino light on flavour ?

Neutrinos lighter because Majorana?

the size of ν Yukawa couplings is alike

Pilar Hernandez drawings

Within seesaw,to that for other fermions:

0.8 0.5 ~ 9º -0.4 0.5 -0.7

-0.4 0.5 +0.7

VPMNS =

~1 λ λ3

λ ~1 λ2

λ3 λ2 ~1

VCKM = λ~0.2

Leptons

Quarks

Why so different?

0.8 0.5 ~ 9º -0.4 0.5 -0.7

-0.4 0.5 +0.7

VPMNS =

~1 λ λ3

λ ~1 λ2

λ3 λ2 ~1

VCKM = λ~0.2

Leptons

Quarks

Perhaps also because νs may be Majorana?

•Dynamical Yukawas

Yukawa couplings are the source of flavour in the SM

YD

YU

QL

QL

UR

DR

H

H

YE

YN

L

L

NR

ER

H

H

(i.e. Seesaw type-I)

Yukawa couplings are a source of flavour in the ν-SM

May they correspond to dynamical fields

(e.g. vev of fields that carry flavor) ?

Instead of inventing an ad-hoc symmetry group,

why not use the continuous flavour group

suggested by the SM itself?

We have realized that the different pattern for

quarks versus leptons

may be a simple consequence of the

continuous flavour group of the SM (+ seesaw)



We have realized that the different pattern for

quarks versus leptons

may be a simple consequence of the

continuous flavour group of the SM (+ seesaw)

Our guideline is to use:

- maximal symmetry - minimal field content



Global flavour symmetry of the SM

* QCD has a global -chiral- symmetry in the limit of massless quarks. For n generations:

* In the SM, fermion masses and mixings result from Yukawa couplings. For massless quarks, the SM has a global flavour symmetry:

SM

fermions

fermions

[Georgi, Chivukula, 1987]

Quarks

Gflavour

This continuous symmetry of the SM

QL DR

H Y spurion

is phenomenologically very successful and

at the basis of Minimal Flavour Violation

in which the Yukawa couplings are only spurions

D’Ambrosio+Giudice+Isidori+Strumia; Cirigliano+Isidori+Grinstein+Wise

Gflavour

This continuous symmetry of the SM

QL DR

H Y spurion

is phenomenologically very successful and

at the basis of Minimal Flavour Violation

in which the Yukawa couplings are only spurions


Gflavour

Υαβ+ Υδγ Qα γµQβ Qγ γµ Qδ Λf2

- -

One step further

(Alonso, Gavela, D.Hernandez, Merlo, Rigolin, 2012 -2013)

(Alonso, Gavela, Isidori, Maiani, 2013)

Quarks

< Y > Λf

< Y > Λf

QL DR

H <Yd >

For this talk:

each YSM -- >one single field Y YSM ~

QL UR

H <Yu >quarks:

Gflavour= SU(3)QL x SU(3)UR x SU(3)DR ....Anselm+Berezhiani 96; Berezhiani+Rossi 01... Alonso+Gavela+Merlo+Rigolin 11...

< Y > Λ< Y > Λf

QL DR

H <Yd >

For this talk:


QL UR

H <Yu >quarks:

Gflavour= SU(3)QL x SU(3)UR x SU(3)DR .... Yd ~ (3,1,3)

Yu ~ (3,3,1)

-- “bifundamentals”

QL DR

H <Yd >

Yd ~ (3,1,3)

QL UR

H <Yu >

¿V(Yd, Yu)?

Gflavour= SU(3)QL x SU(3)UR x SU(3)DR ....

Yu ~ (3,3,1)

- -

QL DR

H <Yd >

Yd ~ (3,1,3)

QL UR

H <Yu >

Gflavour= SU(3)QL x SU(3)UR x SU(3)DR ....

Yu ~ (3,3,1)

- -

* Does the minimum of the scalar potential justify the observed masses and mixings?

V(Yd, Yu)

* Invariant under the SM gauge symmetry

* Invariant under its global flavour symmetry Gflavour

Gflavour= U(3)QL x U(3)UR x U(3)DR

V(Yd, Yu)

* Invariant under the SM gauge symmetry

* Invariant under its global flavour symmetry Gflavour

Gflavour= U(3)QL x U(3)UR x U(3)DR There are as many independent invariants I as physical variables

V(Yd, Yu) = V( I(Yd, Yu))

Minimization

a variational principle fixes the vevs of the Fields

This is an homogenous linear equation;if the rank of the Jacobian ,

Maximum:then the only solution is:

Less than Maximum:then the number of equations reduces to a number equal to the rank

is:

masses, mixing angles etc.

Boundariesfor a reduced rank of the Jacobian,

there exists (at least) a direction for whicha variation of the field variables does

not vary the invariants

that is a Boundary of the I-manifold[Cabibbo, Maiani,1969]

Boundaries Exhibit Unbroken Symmetry [Michel, Radicati, 1969]

(maximal subgroups)

Bi-fundamental Flavour Fields

[Feldmann, Jung, Mannel;Jenkins, Manohar]

For quarks: 10 independent invariants (because 6 masses+ 3 angles + 1 phase) that we may choose as

quark case


masses and mixing[Feldmann, Jung, Mannel; Jenkins, ManoharAlonso, Gavela, Isidori, Maiani 2013]

only masses

quark case

Jacobian Analysis: Mixing

the rank is reduced the most for:

VCKM= PERMUTATION

no mixing: reordering of states

(Alonso, Gavela, Isidori, Maiani 2013)

Quark Natural Flavour Pattern

giving a hierarchical mass spectrum without mixing

a good approximation to the observed Yukawas to order (λC)2

Summarizing, a possible and natural breaking pattern arises:

Gflavour (quarks)

< YD > < YU >

And what happens for leptons ?

Any difference with Majorana neutrinos?

Global flavour symmetry of the SM + seesaw

* In the SM, for quarks the maximal global symmetry in the limit of massless quarks was:

SM

quarks

* In SM +type I seesaw, for leptons

the maximal leptonic global symmetry in the limit of massless light leptons is

-> degenerate heavy neutrinos

Gflavour


Very direct results using the bi-unitary parametrization:

Physical parameters=Independent Invariants

* m e, μ, τ= v yE

mν =Y v2 Y Τ M

*But the relation of Yν with light neutrino masses is through




* m e, μ, τ= v yE






* m e, μ, τ= v yE

UR is relevant for leptons

mν ~Yν v2 Yν Τ = y1 y2 v2 0 11 0

UPMNS = 1 1-1 1

eiπ/4 0 0 e-iπ/4

Degenerate neutrino masses {

M M

* For instance for two generations: O(2)NR

e.g. two families

Generically, O(2) allows : - one mixing angle maximal - one relative Majorana phase of π/2 - two degenerate light neutrinos

Now for three generations and

considering all

possible independent invariants

easier using the bi-unitary parametrization as we did for quarks

Leptons

UL and eigenvalues

UR and eigenvalues

New

Inva

rian

ts w

rt Q

uark

s

Gflavour (leptons) = 3 3 3

Number of Physical parameters = number of Independent Invariants 15 invariants for


same as for VCKM

O(3) vs U(3)

...which is now not trivial mixing...


...in fact it allows maximal mixing:


...in fact it leads to one maximal mixing angle:


and maximal Majorana phase

mν2=mν3

...in fact it leads to one maximal mixing angle:



θ23 =45o; Majorana Phase Pattern (1,1,i)

& at this level mass degeneracy: mν2 = mν3

related to the O(2) substructure [Alonso, Gavela, D. Hernández, L. Merlo;[Alonso, Gavela, D. Hernández, L. Merlo, S. Rigolin]

if the three neutrinos are quasidegenerate, perturbations:

This very simple structure is signaled by the extrema of the potential and

has eigenvalues (1,1,-1)

and is diagonalized by a maximal θ = 45º


3 degenerate light neutrinos+ a maximal Majorana phase

This very simple structure is signaled by the extrema of the potential and

has eigenvalues (1,1,-1)

and is diagonalized by a maximal θ = 45º

=

Generalization to any seesaw model

the effective Weinberg Operator

shall have a flavour structure that breaks U(3)L to O(3)

then the results apply to any seesaw model

v2 Cd=5

Cd=5

mν

First conclusion:

* at the same order in which the minimum of the potential

does NOT allow quark mixing,

it allows:

- hierarchical charged leptons

- quasi-degenerate neutrino masses

- one angle of ~45 degrees

- one maximal Majorana phase and the other one trivial

Perturbations can produce a second large angle


produce a second large angle and a perturbative one together with mass splittings

degenerate spectrum



only thisvanishes with the

perturbations

this angle does not vanish

withvanishing

perturbations


degenerate spectrum




degenerate spectrum

accommodation of angles requires degenerate spectrum at reach in future neutrinoless double β exps.!

rough estimate m~0.1eV

Slide from Laura Baudis talk presenting the new Gerda data at Invisibles13 workshop 3 weeks ago

~ 2 1026 yr

Where do the differences in Mixing originated?

in the symmetries of the Quark and Lepton sectors

for the type I seesaw employed here;

in general

Where do the differences in Mixing originate?

From theMAJORANA vs DIRAC nature of fermions

Conclusions• Spontaneous Flavour Symmetry Breaking is a predictive

dynamical scenario

• Simple solutions arise that resemble nature in first approximation

• The differences in the mixing pattern of Quarks and Leptons arise from their Dirac vs Majorana nature (U vs. O symmetries). O(2) singled out -> O(3).

• A correlation between large angles and degenerate spectrum emerges. Explicitly, for neutrinos we find: fixed Majorana phases (1,1,i) , θ23 =45o, θ12 large, θ13 small and deg. ν’s

• This scenario will be tested in the near future by 0ν2β experiments (~.1eV).... or cosmology!!!

Back-up slides

Fundamental Fields

May provide dynamically the perturbations

In the case of quarks they can give the right corrections:

under study in the lepton sector

[Alonso, Gavela, Merlo, Rigolin]

We set the perturbations by hand. Can we predict them also dynamically?

YD

YU

QL

QL

UR

QLQL

DR

H

H

(1,1,3)

(1,3,1)(3,1,1)

Use the flavour symmetry of the SM with masless fermions:

replace Yukawas by fields:

(3,1,1)

(3,1,1)

(3,1,3)

(3,3,1)

< >

< > Spontaneous breaking of flavour symmetry dangerous

Gf = U(3)Q x U(3)U x U(3)D L RR

Flavour Symmetry Breaking

To prevent Goldstone Bosons the symmetry can beGauged

[Grinstein, Redi, VilladoroGuadagnoli, Mohapatra, Sung

Feldman]

Jacobian Analysis: Masses

IU2

IU33

U�2�2�U�1�

U�3�

U�2��U�1�2

U�2��U�1� U�1�4

U�2��U�1�

[U(3)xU(3) broken to]


Jacobian Analysis: Eigenvalues

IU2

IU33

U�2�2�U�1�

U�3�

U�2��U�1�2

U�2��U�1� U�1�4

U�2��U�1�

[U(3)LxU(3)ER broken to]

Jacobian Analysis: [40 years ago...][Cabibbo, Maiani]Breaking of

-

Lepton Natural Flavour PatternSummarizing, a possible and natural

breaking pattern:

brings along hierarchical charged leptons

and (at least) two degenerate neutrinosand maximal angle and Majorana phase

θ23 =45o; Majorana Phase Pattern (1,1,i)& Mass degeneracy: mν2 = mν3

Boundaries Exhibit Unbroken Symmetry

Extra-Dimensions Example

The smallest boundaries are extremal points of any function

[Michel, Radicati, 1969]

YD

YU

QL

QL

UR

QLQL

DR

H

H

Gf = SU(3)Q x SU(3)U x SU(3)D L RR

(3,1,1) (1,1,3)

(1,3,1)(3,1,1)

~ (3,1,3)

~ (3,3,1)

The non-abelian part of the flavour symmetry of the SM:

broken by Yukawas:

Some good ideas:

Minimal Flavour Violation:

- Use the flavour symmetry of the SM in the limit of massless fermions quarks: Gflavour= U(3)QL x U(3)UR x U(3)DR - Assume that Yukawas are the only source of flavour in the SM and beyond Υαβ+ Υδγ Qα γµQβ Qγ γµ Qδ Λflavour2

... agrees with flavour data being aligned with SM

... allows to bring down Λflavour --> TeV


QL DR

H Y spurion

(Chivukula+ Georgi)

Some good ideas:


- Use the flavour symmetry of the SM in the limit of massless fermions quarks: Gflavour= U(3)QL x U(3)UR x U(3)DR - Assume that Yukawas are the only source of flavour in the SM and beyond Υαβ+ Υδγ Qα γµQβ Qγ γµ Qδ Λflavour2

... agrees with flavour data being aligned with SM

... allows to bring down Λflavour --> TeV

(Chivukula+Georgi 87; Hall+Randall; D’Ambrosio+Giudice+Isidori+Strumia; Cirigliano+Isidori+Grisntein+Wise; Davidson+Pallorini; Kagan+G. Perez + Volanski+Zupan,... )

QL DR

H Y spurion

Lalak, Pokorski, Ross; Fitzpatrick, Perez, Randall; Grinstein, Redi, Villadoro

(Chivukula+ Georgi)

YD

YU

QL

QL

UR= (c, s, t)R

QLQL

DR = (d, s, b)R

H

H


(1,1,3)

(1,3,1)(3,1,1)


which is broken by Yukawas:

(3,1,1)

(3,1,1)

~ (3,1,3)

~ (3,3,1)

YD

YU

QL

QL

UR

QLQL

DR

H

H

(1,1,3)

(1,3,1)(3,1,1)


replace Yukawas by fields:

(3,1,1)

(3,1,1)

(3,1,3)

(3,3,1)

< >

< >


Flavour FieldsThe Yukawa Operator has to be explicitly flavour invariant

at high energies

A single and therefore “bi-fundamental” field

(d=5)

(QL)!(DR)"

H(YD)!"



These are (proportional to):

3 masses in de up sector, 3 masses in de down sector, 4 mixing parameters in VCKM

Yd Yu

<Yd> <Yu>

for the sub-Jacobian which involves only masseswe can identify the shape of the I-manifold

Jacobian Analysis


Renormalizable Potential

Invariants at the Renormalizable Level


with the definition

the potential

which contains 8 parametersmass spectrum


with the definition

the potential

which contains 8 parameters

mixing

Tr(Yu Yu+ Yd Yd+)

e.g. for the case of two families:

mq

θ

V

at the minimum:

same conclusion for 3 families

Berezhiani-Rossi; Anselm, Berezhiani; Alonso, Gavela, Merlo, Rigolin

;

-> NO MIXING

Von Neumann Trace Inequality

Renormalizable Potential, mixing three families

So the Potential selects:

“normal”Hierarchy

“inverted”Hierarchy

No mixing, independently of the mass spectrum

coefficient in the potential

Tr(Yu Yu+ Yd Yd+)

e.g. for the case of two families:

mq

θ

V

at the minimum:

same conclusion for 3 families

Berezhiani-Rossi; Anselm, Berezhiani; Alonso, Gavela, Merlo, Rigolin

;

-> NO MIXING

Using Casas-Ibarra parametrization Yν= UPMNS mν1/2 R MN1/2

Tr(YE YE+ Yν Yν+) = Tr( mi1/2 U+ ml

2 U mi1/2 R+ ΜΝ R)

diagonal eigenvalues

with ω real,

* In degenerate limit of heavy neutrinos MN1=MN2=M

ch ω -i sh ω

i sh ω ch ω ( )R = with ω real,

it follows that:

2 families, leptons; let us analyze the mixing invariant

complex orthogonal; it encodes our ignorance of the high energy theory

for 2 generations, the mixing terms in V(YE, Yν) is :

Tr(YE YE+ Yν Yν+)

Tr(Yu Yu+ Yd Yd+)

Leptons

Quarks

cosθ sinθ -sinθ cosθ

e-iα 0 0 eiαwhere UPMNS=

Tr(YE YE+ Yν Yν+)

e.g., for 2 generations, the mixing terms in V(YE, Yν) is :

Tr(Yu Yu+ Yd Yd+)

This mixing term unphysical if either “up” or “down” fermions degenerate

Mixing physical even with degenerate neutrino masses,if Majorana phase non-trivial

Leptons

Quarks

Tr(YE YE+ Yν Yν+)

Tr(YE YE+ Yν Yν+)

α= π/4 or 3π/4

Minimisation

*

*

Large angles correlated with degenerate masses

Maximal Majorana phase


tgh 2ω

(for non trivial sin2ω)

sin2ω

The flavour symmetry is Gf =

which adds a new invariant for the lepton sector. In total:

Tr ( YE YE+ )

Tr ( Yν Yν+ )

mixingTr ( YE YE+ Yν Yν+ )

Tr ( YE YE+ )2

Tr ( Yν Yν+ )2

Tr ( Yν+Yν YνT Yν* ) <-- Ο(2)N

Example: 2 families; consider the renormalizable set of invariants:


which adds a new invariant for the lepton sector. In total:

Tr ( YE YE+ )

Tr ( Yν Yν+ )


Tr ( YE YE+ )2

Tr ( Yν Yν+ )2

<-- Ο(2)N

Example: 2 families; consider the renormalizable set of invariants:

Tr ( Yν+Yν (Yν+ Yν)T )

Tr(YE YE+ Yν Yν+)

α= π/4 or 3π/4

Minimisation of

Large angles correlated with degenerate masses

Maximal Majorana phase


tgh 2ω

cosθ sinθ -sinθ cosθ

e-iα 0 0 eiαwhere UPMNS=

Jacobian


What is the symmetry in this boundary?

which is extended if the eigenvalues are degenerate

[Alonso, Gavela, G. Isidori, L. Maiani]

hU

hD

I

II

III

IV

Renormalizable Potential, masses

Renormalizable Potential, Stability

This region’s sizenonetheless

depends on the restof paramters (λ,g)

hU

hD

I

II

III

IV


defining

the potential reads:

9 parameters

hΝ

hE

I

II

III

IV

VII

VI

VVIII

Renormalizable Potential: Masses


defining

the potential reads:

9 parameters

Renormalizable Potential: Mixing

One maximal angle again

but not quite in the right place

The solution with a maximal θ23 , may arise in a Non-Renormalizable

Potential or could be a Local Minimaof the Renormalizable Potential

O(2), SU(n), O(n) .... ?

* What is the role of the neutrino flavour group?

Leptons: Gflavour = U(2)L x U(2)ER x ?

Inmediate results using for both quark and leptons Y= UL ydiag UR

To analyze this in general, use common parametrization for quarks and leptons:

Y = UL ydiag. UR

* Quarks, for instance: UR unphysical, UL --> UCKM

YD = UCKM diag(yd, ys, yb) ; YU = diag(yu, yc, yt)

* Leptons: YE = diag(ye, yµ, yτ) ; Yν = UL ydiag. UR

UPMNS diagonalize UL yνdiag. UR v2 URT yνdiag. ULT


mν ~Yν v2 Yν Τ = M M

U(n)


U(n)


U(3)L x U(3)ER x U(2)NRi.e.:

or: U(3)L x U(3)ER x U(3)NR


e.g. generic seesaw

M

with M carrying flavour M spurion

More invariants in this case:

Tr ( YE YE+ )

Tr ( Yν Yν+ )Tr ( YE YE+ Yν Yν+ )Tr ( YE YE+ )2

Tr ( Yν Yν+ )2

Tr ( MN MN+ ) Tr ( MN MN+ ) 2 Tr ( MN MN+ Yν+Yν )

e.g. U(n)NR ... leptons

Result: no mixing for flavour groups U(n)


e.g. generic seesaw

with M carrying flavour M spurion

More invariants in this case:

Tr ( YE YE+ )

Tr ( Yν Yν+ )Tr ( YE YE+ Yν Yν+ )Tr ( YE YE+ )2

Tr ( Yν Yν+ )2

Tr ( MN MN+ ) Tr ( MN MN+ ) 2 Tr ( MN MN+ Yν+Yν)

e.g. SU(n)NR ... leptons

* Tr ( Yν Yν+ YΕ YΕ+ ) = Tr ( UL yνdiag. 2 UL + yldiag. 2) At the minimum:

UL=1

* Tr ( MN MN+ Yν Yν+ ) = Tr ( UR yνdiag. 2 UR + Midiag. 2) UR=1

M

Y = UL ydiag. UR

* Quarks, for instance: UR unphysical, UL --> UCKM

YD = UCKM diag(yd, ys, yb) ; YU = diag(yu, yc, yt)

Tr ( Yu Yu+ Yd Yd+ ) = Tr ( UL yudiag. 2 UL + yddiag. 2)

UL=U CKM ~1 at the minimum

NO MIXING

same conclusion for 3 families of quarks:

Can its minimum correspond naturally to the observed masses and mixings?

i.e. with all dimensionless λ’s ~ 1

and dimensionful µ´s Λf<=

* 3 generations: for the largest fraction of the parameter space, the stable solution is a degenerate spectrum

( )yuyc

yt( )y

yy

instead of the observed hierarchical spectrum, i.e.

~

( )yuyc

yt( )0

0y~

(at leading order)

Spectrum for flavons Σ in the bifundamental:Y --> one single field Σ

ie, the u-part:

Spectrum: the hierarchical solution is unstable in most of the parameter space.

Stability:

µ2/µ2~

Hierarchical dominates

Degenerate dominates

ie, the u-part:

Spectrum: the hierarchical solution is unstable in most of the parameter space.

Stability:

µ2/µ2~

Hierarchical dominates

Degenerate dominates

Nardi emphasized this solution (and extended the analysis to include also U(1) factors)

Y --> one single field Σ

The invariants can be written in termsof masses and mixing

* two families:

< Σd > = Λf . diag (yd ) ; < Σu > = Λf .VCabibbo diag(yu )

VCabibbo =

<Tr ( Σu Σu+ )> = Λf 2 (yu2 +yc2) ; <det ( Σu )> = Λf 2 yuyc

<Tr ( Σu Σu+ Σd Σd+ )>=Λf4 [( yc2 - yu2) ( ys2 - yd2) cos2θ +...]/2

(Alonso, Gavela, Merlo, Rigolin, arXiv 1103.2915)

Non-degenerate masses No mixing !

Notice also that ~ (Jarlskog determinant)




e.g. adding non-renormalizable terms... NO




e.g. adding non-renormalizable terms...


* To accomodate realistic mixing one must introduce wild fine tunnings of O(10-10) and nonrenormalizable terms of dimension 8

* Without fine-tuning, for two families the spectrum is degenerate

NO

(Alonso, Gavela, Merlo, Rigolin)

Y --> one single field Σ three families

* at renormalizable level: 7 invariants instead of the 5 for two families

Interesting angular dependence:

The real, unavoidable, problem is again mixing:

* Just one source:

Tr ( Σu Σu+ Σd Σd+ ) = Λf4 (P0 + Pint)

Sad conclusions as for 2 families: needs non-renormalizable + super fine-tuning

*a good possibility for the other angles :

Yukawas --> add fields in the fundamental of the flavour group

1) Y -- > one single scalar Y ~ (3, 1, 3)

2) Y -- > two scalars χ χ+ ~ (3, 1, 3)

×

χ ×

Ψ ×3) Y -- > two fermions ΨΨ ~ (3, 1, 3)_

Y


2) Y -- > two scalars χ χ+ ~ (3, 1, 3)

χ ~ (3, 1, 1)

×

χ ×


Y


2) Y -- > two scalars χ χ+ ~ (3, 1, 3)

χ ~ (3, 1, 1)

Y ×

χ ×


d=5 operator

d=6 operator

d=7 operator

✝

χ × Y --> quadratic in fields χ

Y ~< χ χ >Λf

2

Holds for 2 and 3 families !

Automatic strong mass hierarchy and one mixing angle already at the renormalizable level

✝

χ × 2) Y --> quadratic in fields χ

Y ~< χ χ >Λf

2

i.e. YD ~ χLd (χRd )+ ~ (3, 1, 1) (1, 1, 3) ~ (3, 1, 3)

Λf2

( a , b , c .......)

Y --> quadratic in fields χ

f f

Towards a realistic 3 family spectrum

e.g. replicas of χL , χR , χRu d

???

Suggests sequential breaking:

SU(3)3 SU(2)3 ............ mt, mb mc, ms, θC


* From bifundamentals: <Yu> =

<Yd> =

00

00

* From fundamentals χ : yc, ys and θC


e.g. replicas of χL , χR , χRu d

???

Suggests sequential breaking:

SU(3)3 SU(2)3 ............ mt, mb mc, ms, θC


Maybe some connection to: Berezhiani+Nesti; Ferretti et al., Calibbi et al. ??

* At leading (renormalizable) order:

* The masses of the first family and the other angles from non-renormalizable terms or other corrections or replicas ?

without unnatural fine-tunings

....and analogously for leptonic mixing ?

<Yu>

<Yd>

i.e. for quarks, a possible path:


i.e. combining d=5 and d =6 Yukawa operators

Y --> linear + quadratic in fields

Low M, large Y is typical of seesaws with approximate Lepton Numberconservation

U(1)LN

Wyler+Wolfenstein 83, Mohapatra+Valle 86, Branco+Grimus+Lavoura 89, Gonzalez-Garcia+Valle 89, Ilakovac+Pilaftsis 95, Barbieri+Hambye+Romanino 03, Raidal+Strumia+Turzynski 05, Kersten+Smirnov 07, Abada+Biggio+Bonnet+Gavela+Hambye 07, Shaposhnikov 07, Asaka+Blanchet 08, Gavela+Hambye+D. Hernandez+ P. Hernandez 09

(-> ~ degenerate heavy neutrinos)

LHC is more competitive for concrete seesaw models:

These models separate the flavor and the lepton number scale

For instance, in the minimal seesaw I, Lepton number scale and flavour scale linked:

MT

M

Y

YT

seesaw I

mν =Y v2 Y Τ M UlN ~

YvM

UlN

l+

N


e.g. seesaw with approximately conserved lepton number e.g. O(2)NR ... leptons

MT

M


e.g. seesaw with approximately conserved lepton number e.g. O(2)NR ... leptons

< YE > < Yν >

< YE > < Yν >

me

mµ

mτ

α= π/4 or 3π/4y2-y’2

y2-y’2

*In the O(2)model used before: tgh 2ω = and y2-y’2

y2-y’2

*If we had used instead a flavor SU(2)model sinh 2ω =0 -->NO MIXING

* e-µ, µ-τ etc. oscillations and rare decays studied: Gavela, Hambye, Hernandez2 ; .....

Gavela, Hambye, Hernandez2 ;

* Alonso + Li, 2010, MINSIS report: possible suppresion of µ-e transitions for large θ13

Gavela, Hambye, Hernandez2 ;

cancellationsfor large θ13

* e-µ, µ-τ etc. oscillations and rare decays studied: Gavela, Hambye, Hernandez2 09 ; .....

* Alonso + Li, 2010: possible suppresion of µ-e transitions ->important impact of νµ - ντ at a near detectors

* e-µ, µ-τ etc. oscillations and rare decays studied: Gavela, Hambye, Hernandez2 09; .....

* Alonso + Li, 2010: possible suppresion of µ-e transitions ->important impact of νµ - ντ at a near detectors

Eboli, Gonzalez-Fraile, Gonzalez-Garcia

For type III version of our 2 N model, signals observable at LHC up to Λ~ 500 GeV for 30 fb-1

Nee

Neµ

Neτ

α α <-- Majorana phase

Some good ideas:

“Partial compositeness”:

D.B. Kaplan-Georgi in the 80s proposed a composite Higgs:

* Higgs light because the whole Higgs doublet is multiplet of goldstone bosons They explored SU(5)--> SO(5). Explicit breaking of SU(2)xU(1) symmetry via external gauged U(1) Nowadays SO(5)--> SO(4) and explicit breaking via SM weak interaction (Contino, Nomura, Pomarol; Agashe, Contino, Pomarol; Giudice, Pomarol, Ratazzi, Grojean; Contino, Grojean, Moretti; Azatov, Galloway, Contino...) SO(6) --> SO(5) to get also DM (Frigerio, Pomarol, Riva, Urbano)

(Kaplan, Georgi, Dimopoulos, Banks, Dugan, Galison)

~1

Anarchy: alive with not so small θ13 and not θ23 not maximal

~1

~1

~1

~1 ~1

~1~1

~1

mν ~

no symmetry in the lepton sector, just random numbers

(Hall, Murayama, Weiner; Haba, Murayama; De Gouvea, Murayama... Going towards hierarchy: Altarelli, Feruglio, Masina, Merlo)

- Does not relate mixing to spectrum- Does not address both quarks and leptons

*3 families with O(2)NR :

- 3 light + 2 heavy N degenerate: bad θ12 quadrant. It cannot accomodate data!

- 3 light + 3 heavy N : OK for θ23 maximal and spectrum

*What about the other angles?

experimentally sin2θ23= 0.41 +-0.03 or 0.59+-0.02 Gonzalez-Garcia, Maltoni, Salvado, Schwetz Sept. 2012

( O(2) )0 0

3x3

*3 families with O(2)NR :

- 3 light + 2 heavy N degenerate: bad θ12 quadrant. It cannot accomodate data!

- 3 light + 3 heavy N : OK for θ23 maximal and spectrum

*What about the other angles?

experimentally sin2θ23= 0.41 +-0.03 or 0.59+-0.02 Gonzalez-Garcia, Maltoni, Salvado, Schwetz Sept. 2012

Moriond this morning, T2K best fit point sin22θ23=1.00 -0.068 90%CL -> 45º !

BSM electroweak

* HIERARCHY PROBLEM Fine-tuning issue: if BSM physics, why Higgs so light

Interesting mechanisms to solve it: SUSY, strong-int. light Higgs, extra-dim….

In practice, none without further fine-tunings

BSM electroweak




* FLAVOUR PUZZLE: ~no theoretical progress

New B physics data AND neutrino masses and mixings

Understanding of the underlying physics stalled since 30 years. BSM theories tend to make it worse.

BSM electroweak




* FLAVOUR PUZZLE : no progress

New B physics data AND neutrino masses and mixings

Understanding of the underlying physics stalled since 30 years. BSM theories tend to make it worse.

Λelectroweak ~ 1 TeV ?

Λf ~ 100’s TeV ???

The FLAVOUR WALL for BSM

i.e susy MSSM:

competing with SM at one-loop

i.e susy MSSM:

ii) FCNC

< 1 loop in SM ---> Best (precision) window of new physics

i) Typically, BSMs have electric dipole moments at one loop

The FLAVOUR WALL for BSM

i.e susy MSSM:

competing with SM at one-loop

i.e susy MSSM:

ii) FCNC

< 1 loop in SM ---> Best (precision) window of new physics

i) Typically, BSMs have electric dipole moments at one loop

conversion (MEG, µ2e...)

What happens if we add

non-renormalizable terms to the potential?

In fact one should consider as many invariants as physical variables

Just TWO heavy neutrinos

Raidal, Strumia, TurszynskiGavela, Hambye, Hernandez2

MM

Lepton number scale and flavour scale distinct

seesaw I with


MM

mν = Y v2 Y´ Τ M UlN ~ Y

M--> Lepton number conserved conserved if either Y or Y’ vanish:

Raidal, Strumia, TurszynskiGavela, Hambye, Hernandez2

Gavela, Hambye, Hernandez2

Raidal, Strumia, Turszynski

--> One massless neutrino and only one Majorana phase α


MM

Comparing the scales reached by

Neutrino Oscillations vs µ-e experiments vs LHC

e.g. in Seesaw type I scales (heavy singlet fermions)

* ν-oscillations: 10-3eV - MGUT ~ 1015 GeV, because interferometry

* µ-e conversion: 2MeV - 6000 GeV

* LHC: ~ # TeV


adds a new invariant for the lepton sector, in total:

Tr ( YE YE+ )

Tr ( Yν Yν+ )


Tr ( YE YE+ )2

Tr ( Yν Yν+ )2

Tr ( Yν σ2Yν+ ) 2 <-- Ο(2)N

Ο(2)N is simply associated to Lepton Number

Leptons


MM

(Alonso, Gavela, D. Hernandez, Merlo, Rigolin)


Leptons


MM




MM



What is the symmetry in this boundary?

related to the O(2) substructure

[Alonso, Gavela, D. Hernández, L. Merlo;[Alonso, Gavela, D. Hernández, L. Merlo, S. Rigolin]

In many BSM the Yukawas do notcome from dynamical fields:

Some good ideas: D.B. Kaplan-Georgi in the 80’s proposed a light SM scalar because being a (quasi) goldstone boson: composite Higgs

(D.B. Kaplan, Georgi, Dimopoulos, Banks, Dugan, Galison.......Contino, Nomura, Pomarol; Agashe, Contino, Pomarol; Giudice, Pomarol, Ratazzi, Grojean; Contino, Grojean, Moretti; Azatov, Galloway, Contino... Frigerio, Pomarol, Riva, Urbano...)

Some good ideas: D.B. Kaplan-Georgi in the 80’s proposed a light SM scalar because being a (quasi) goldstone boson: composite HiggsFlavour “Partial compositeness” D.B Kaplan 91:

mq= v YSM

QL UR

H YSM

(D.B Kaplan 91; Redi, Weiler; Contino, Kramer, Son, Sundrum; da Rold, Delauney, Grojean, G. Perez; Contino, Nomura, Pomarol, Agashe, Giudice, Perez, Panico, Redi, Wulzer...)

A sort of “seesaw for quarks” (nowadays sometimes justified from extra-dim physics )


QL UR

H

YSM = YΔL ΔR/M2

YMΔL ΔR

mq= v YSM



Some good ideas: D.B. Kaplan-Georgi in the 80’s proposed a Higgs light because being a (quasi) goldstone boson: composite Higgs


QL UR

H

YSM = YΔL ΔR/M2

YMΔL ΔR

mq= v YSM


Neutrino masses:

L

H H

Ld=5 Weinberg operator




QL UR

H

YSM = YΔL ΔR/M2

YMΔL ΔR

mq= v YSM


Neutrino masses:


YM

YxL

H H

mν= Y v2/M YT

type I

L



QL UR

H

YSM = YΔL ΔR/M2

YMΔL ΔR

mq= v YSM


Neutrino masses:


M

YL

H H

mν= Y µ v2/M2

µtype II

L


For instance, in discrete symmetry ideas:

The Yukawas are indeed explained in terms of dynamical fields. And they do not need to worry about goldstone bosons.

In spite of θ13 not very small, there is activity.For instance, combine generalized CP (Bernabeu, Branco, Gronau 80s) with discrete Z2 groups in the neutrino sector : maximal θ23, strong constraints on values of CP phases (Feruglio, Hagedorn and Ziegler 2013; Holthausen, Lindner and Schmidt 2013)

But:- Discrete approaches do not relate mixing to spectrum- Difficulties to consider both quarks and leptons

They were popular mainly because they can lead easily to large mixings (tribimaximal, bimaximal...)

Some good ideas:

- Use the flavour symmetry of the SM in the limit of massless fermions quarks: Gflavour= U(3)QL x U(3)UR x U(3)DR

U(2) (Pomarol, Tomasini; Barbieri, Dvali, Hall, Romanino...).... U(2)3 (Craig, Green, Katz; Barbieri, Isidori, Jones-Peres, Lodone, Straub..

..Sala) Sequential ideas (Feldman, Jung, Mannel; Berezhiani+Nesti; Ferretti et al.,

Calibbi et al. ...)

QL DR

H Y

Hybrid dynamical-non-dynamical Yukawas:

U(2)0 0 1

spurion

(Chivukula+ Georgi)


For this talk:


< Y > Λfl

Alonso, B.G., D. Hernandez, L. Merlo, Rigolin

Can it shed light on why quark and neutrino mixings are so different?

QL DR

H < > <-->YD

Assume that the Yukawa couplings correspond to dynamical fields at high energies .......

YSM ~ < φ > or YSM ~ 1/< φ > or ...... < (φ χ)n>

(Alonso+Gavela+Merlo+Rigolin 11) ...

[Cabibbo,Michel,+Radicati, Cabibbo+Maiani ...

C. D. Froggat, H. B. NielsenAnslem+Berezhiani, Berezhiani+Rossi]

For this talk:


< Y > Λf

Anselm+Berezhiani 96; Berezhiani+Rossi 01... Alonso+Gavela+Merlo+Rigolin 11...

transforming under the SM flavour group

=

Generalization to any seesaw model

the effective Weinberg Operator

shall have a flavour structure that breaks U(3)L to O(3)

then the results apply to any seesaw model

This did not need any ad-hoc discrete symmetries, but simply using the in-built continuous flavour symmetry of the SM + seesaw, U(3)5 x O(3)

Also, note that often people working with “flavons” invents a “texture” that goes well with data, and then tries to designa potential that leads to it. In our case, the inevitable potential minima encompass the different patterns of quarks and leptons.

Some good ideas, based on continuous symmetries:

Frogatt-Nielsen ‘79: U(1)flavour symmetry

- Yukawa couplings are effective couplings,- Fermions have U(1)flavour charges

< φ > n Q H qR , Y ~ < φ > nn Λ Λ

e.g. n=0 for the top, n large for light quarks, etc.

--> FCNC ?

QL DR

H φ’s

In some BSM theories, Yukawas do correspond to dynamical fields:

- for instance in discrete symmetry scenarios

- also with continuous symmetries

Neutrinos and the Flavour Puzzlevietnam.in2p3.fr/2013/Inauguration/transparencies/Gavela.pdf[Alonso,...

Documents

Transcript of Neutrinos and the Flavour Puzzlevietnam.in2p3.fr/2013/Inauguration/transparencies/Gavela.pdf[Alonso,...